Deterministic Non-linear Topological Earthquake Control System Based on Rough Operator Algebra (ROA) and Seonggil Field Equations (SFE)

This paper proposes a deterministic non-linear topological control system to overcome the low-frequency, long-period pulses and non-linear perturbations applied to structures during mega-earthquakes. We introduce the Rough Operator Algebra (ROA) framework, which reinterprets input acceleration as an orthogonality defect within a multidimensional state space. Overcoming the limits of classical continuous calculus via Advanced Rough Calculus (ARC), we integrate the Seonggil Field Equations (SFE) Zeta-Resonance thermodynamic active control. Crucially, an 8th-power scale non-linear thermodynamic damping is applied,mathematically corresponding to the volumetric distortion of an 8-dimensional topological tensor space.A rigorous mathematical proof using Lyapunov stability criteria demonstrates that the building’s residual drift converges asymptotically to zero. These analytical derivations are rigorously corroborated by explicit multi-degree-of-freedom numerical simulations.